168 ON THE COLOUKS OF THICK PLATES. i i - 1 and for the bright ring of the order n, ef^t/n.e^. The formula (14) has already been discussed by Sir John Herschel/aud compared with Newton's measures, with which it manifests a very close agreement. With white light, only a moderate number of rings can be seen, on account of the variation of the scale of the system depending on a variation in the refrangibility of the component parts of which white light is made up. When the rings were formed in air, and the source of light was the flame of an oil-lamp with a small wick, I have counted seven or eight surrounding the central bright spot. But when the system is viewed through a prism, or when the flame of a spirit-lamp is used, an immense number of rings may be seen. 7. Next, suppose the luminous point out of the axis. Referring to the formula (5), we see that the retardation is not now equal to zero at the axis, but throughout a circle whose radius ef is equal to 0. Hence the achromatic line* of the system, which was formerly reduced to a point, is now a circle having its centre in the axis, and passing through the luminous point and its image, which are situated at the opposite extremities of a diameter. The fringes of the first order will be a pair of circles having their centre in the axis, and lying, one outside, and the other inside the central fringe : the fringes of the second order will be another pair of circles lying, one outside the larger, and the other inside the smaller fringe of the first order, and so on. It is to be remarked, however, that only a finite number of fringes are formed inside the central white fringe. If the value of R when e' = 0 be denoted by — w0X, nQ will be a numerical quantity, a function of \} which determines the number of fringes and the fraction of a fringe, belonging to the light of which the wave-length is X, which are formed inside the central white fringe. The value of n0 may be got from equation (5) on putting e = 0, which gives If white light be used, and if nQ exceed 8 or thereabouts lor rays of * I use this term to denote the locus of the points for which the retardation is equal to zero, which forms a curve on either side of which the colours are arranged in descending order.